Ok so I know I keep saying my next video is going to be a papercraft scutoid tutorial
but I can’t help myself because I have an idea I really want to try.
So you know how last time we made monkeybread and talked about how the random balls of dough
expand into shapey shapes, also there was lots of melted butter and I love how melted
butter looks in VR so I wanted to do more of that or if you’re on desktop just click
and drag the screen to see where I am pouring brown sugar butter stuff over this pan full
of pre-prepared refrigerated biscuit dough.
To start with, we’re making simple cinnamon skin cake. Which is definitely not what we’re
calling it, maybe Epithelium Cake? but I’m thinking of each biscuit as a a cell that
we bake into a sheet of cells, like an epitheli-yum.
Anyway the shapes are pretty predictable: when you have four biscuit blobs where the
centers are in a kind of diamond shape like this, then the close opposites are gonna touch
and squish together, while the far opposites are gonna not touch. In this example, the
far opposites end up being pentagonal prisms and the close pair are hexagonal prisms because
of the extra squish face.
So flat sheets of cells are one thing but what if it were curved, or if it wrapped around
into a tube? So let’s get back to the bundt pan, and imagine it’s a section of a simple
epithelial tube. Cells in the body have to make tubes sometimes, right? So each cell
needs to touch both the inside ring and outside ring of the bundt cake for it to be the kind
of epic epithelium that’s totally tubular.
One thing you might notice is that these cells are gonna have to be bigger on the outside
end than the inside end. So what kind of shapes should we expect?
While that’s baking, let’s take another look at our diagrams. Let’s say this diamond
arrangement of cell centers is on the outer surface. And if the cells go straight through
to the center, the inner surface should be the same arrangement except squashed into
the smaller radius of the inner tube, which we can roughly measure out to make this squashed
diamond arrangement.
And that’s when something strange happens. If you don’t think about it too hard, you
might think that whatever the cells look like on the outside, it will look the same but
squashed smaller on the inside. Which might be the case sometimes, but there’s another
kind of thing that can happen.
For this particular diamond where the long way points around the tube on the outside,
well, once it gets squashed now it’s the other kind of diamond where the long way points
along the tube on the inside, and look what happens: the two close cells on the outside
with hexagon ends will end up not touching on the inside of the tube and have pentagon
ends. Meanwhile the two cells that don’t touch on the outside and have pentagon ends
will be closer on the inside of the tube and squish together to have hexagon ends.
So what kind of shape has a hexagon on one end and a pentagon on the other?
Why, doesn’t that sound a lot like our friend the Scutoid?
And in fact, this cylinder argument is from the original Scutoid paper, it’s legit math,
but here’s the important thing: on the outside, there’s a pair of cells that don’t touch,
and that means they can’t communicate directly. But on the inside, it turns out that they
do touch and can communicate though that special scutoidy triangle face. The topology of scutoidal
cell arrangements creates network possibilities you won’t find in a prismy cell arrangement.
What I don’t know is whether the theory is bake-able but let’s dissect our epic
epithelium cake to see if our scutoid construction is gastronomically sound.
We might not get perfect pretty scutoids but what we’re looking for is that extra triangle
face that lets four dough bits all share faces with each other while still being efficient
cell shapes. See, here’s the kind of thing we’re looking for: look at this set of doughbits
where on the outside of the ring the two on the side don’t touch because the bottom
one puffs through to smoosh into the one that was above it, while on the inside the two
on the side squish together to touch while the top and bottom ones don’t. In fact I
am quite pleased to find a few examples of this kind of arrangement.
They may not be as perfect as a paper model but to me, this little scutoidy triangle of
dough-smush represents a tiny piece of the puzzle of life. Cells can’t step back and
see whether they’re part of something that looks like a tube, they don’t have eyes
or brains to help map out whether they're in the right place to help form something
as complicated as a human being, or a dog full of needs and desires. Yet somehow these
cells do find the right place and do form incredibly complicated structures from only
local information. How does that work? I don’t know but maybe scutoids are part of it, maybe
a cell can look at its neighbors and say “hey, we’re in scutoid formation, we must be part
of a tube, I can’t see the whole tube but I know I’m supposed to be part of one so
at least I know I’m doing my part and if we all just do our parts then maybe, just
maybe, together we’ll create something incredible even if we can’t see it or understand it.
And I know there’s things I can’t change, there’s billions of other cells responding
to forces beyond my control, but as long as I do my part and help my neighbors do theirs,
life will go on.”